Simplify the following expression: $p = \dfrac{-64n^2 + 40n}{8n^2 - 72n}$ You can assume $n \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-64n^2 + 40n = - (2\cdot2\cdot2\cdot2\cdot2\cdot2 \cdot n \cdot n) + (2\cdot2\cdot2\cdot5 \cdot n)$ The denominator can be factored: $8n^2 - 72n = (2\cdot2\cdot2 \cdot n \cdot n) - (2\cdot2\cdot2\cdot3\cdot3 \cdot n)$ The greatest common factor of all the terms is $8n$ Factoring out $8n$ gives us: $p = \dfrac{(8n)(-8n + 5)}{(8n)(n - 9)}$ Dividing both the numerator and denominator by $8n$ gives: $p = \dfrac{-8n + 5}{n - 9}$